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A new characteristic property of Mittag-Leffler functions and fractional cosine functions

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Mei Z.-D., Peng J.-G., Jia J.-X.

Studia Mathematica

2014

tom 220

nr 2

119-140

A new characteristic property of the Mittag-Leffler function $E_{α}(at^{α})$ with 1 < α < 2 is deduced. Motivated by this property, a new notion, named α-order cosine function, is developed. It is proved that an α-order cosine function is associated with a solution operator of an α-order abstract Cauchy problem. Consequently, an α-order abstract Cauchy problem is well-posed if and only if its coefficient operator generates a unique α-order cosine function.

Ograniczanie wyników

1 Studia Mathematica

1 Jia J.-X.

1 Mei Z.-D.

1 Peng J.-G.

1 2014

Wyniki wyszukiwania

A new characteristic property of Mittag-Leffler functions and fractional cosine functions